Let｛X_n｝ be a sequence of semimartingale in a filtered complete probability space (Ω，F，F，P) satisfying the usual condition. We use the general Girsanov thorem and closed graph theorem to prove that the sequence ｛X_n｝converges on X in the Emery topology w.r.t Q if｛X_n｝ converges on X in the Emery topology w.r.t P and the probability measureQ^loc《P. In light of this fact, we prove that if X is a d-dimensional semimartingale and a d-dimensional predictable process，H is X-integrable in the sense of vector stochastic integrals w.r.t P， when the probability measure Q^loc《P, H is also X-integrable in the sense of vector stochastic integrals w.r.t Qand these two integrals are Q-differentiable. It is noted that the condition of Q《P is stronger than that of Q^loc《P, therefore, this paper generalizes lemma 4.9 and theorem 4.14 in［1］.